Spikes in two coupled nonlinear Schrödinger equations

Tai-Chia Lin1, Juncheng Wei2
1Department of Mathematics, National Taiwan University, Taipei, Taiwan
2Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

Tài liệu tham khảo

Bates, 2000, Equilibria with many nuclei for the Cahn–Hilliard equation, J. Differential Equations, 160, 283, 10.1006/jdeq.1999.3660 Bates, 1999, Multi-spike stationary solutions of the Cahn–Hilliard equation in higher-dimension and instability, Adv. Differential Equations, 4, 1, 10.57262/ade/1366291798 Conti, 2002, Nehari's problem and competing species system, Ann. Inst. H. Poincaré, 19, 871, 10.1016/S0294-1449(02)00104-X del Pino, 1999, Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting, Indiana Univ. Math. J., 48, 883, 10.1512/iumj.1999.48.1596 del Pino, 1999, On the role of mean curvature in some singularly perturbed Neumann problems, SIAM J. Math. Anal., 31, 63, 10.1137/S0036141098332834 del Pino, 2000, On the role of distance function in some singularly perturbed problems, Comm. Partial Differential Equations, 25, 155, 10.1080/03605300008821511 del Pino, 2000, Multiple peak solutions for some singular perturbation problems, Cal. Var. Partial Differential Equations, 10, 119, 10.1007/s005260050147 Donley, 2001, Dynamics of collapsing and exploding Bose–Einstein condensates, Nature, 19, 295, 10.1038/35085500 Dancer, 1999, On the location of spike s of solutions with two sharp layers for a singularly perturbed semilinear Dirichlet problem, J. Differential Equations, 157, 82, 10.1006/jdeq.1998.3619 Dancer, 1999, Multipeak solutions for a singular perturbed Neumann problem, Pacific J. Math., 189, 241, 10.2140/pjm.1999.189.241 Estaban, 1982, Existence and non-existence results for semilinear problems in unbounded domains, Proc. Roy. Soc. Edinburgh Sect. A, 93, 1, 10.1017/S0308210500031607 Esry, 1997, Hartree–Fock theory for double condensates, Phys. Rev. Lett., 78, 3594, 10.1103/PhysRevLett.78.3594 Gidas, 1981, Symmetry of positive solutions of nonlinear elliptic equations in Rn, vol. 7A, 369 Gui, 1999, Multiple interior spike solutions for some singular perturbed Neumann problems, J. Differential Equations, 158, 1, 10.1016/S0022-0396(99)80016-3 Gui, 2000, On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems, Canad. J. Math., 52, 522, 10.4153/CJM-2000-024-x Gui, 2000, Multiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 17, 249, 10.1016/S0294-1449(99)00104-3 Grossi, 2000, Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Cal. Var. Partial Differential Equations, 11, 143, 10.1007/PL00009907 Gupta, 2003, Radio-frequency spectroscopy of ultracold fermions, Science, 300, 1723, 10.1126/science.1085335 Hall, 1998, Dynamics of component separation in a binary mixture of Bose–Einstein condensates, Phys. Rev. Lett., 81, 1539, 10.1103/PhysRevLett.81.1539 Kwong, 1989, Uniqueness of positive solutions of Δu−u+up=0 in Rn, Arch. Rational Mech. Anal., 105, 243, 10.1007/BF00251502 Li, 1998, On a singularly perturbed equation with Neumann boundary condition, Comm. Partial Differential Equations, 23, 487, 10.1080/03605309808821354 Li, 1998, The Dirichlet problem for singularly perturbed elliptic equations, Comm. Pure Appl. Math., 51, 1445, 10.1002/(SICI)1097-0312(199811/12)51:11/12<1445::AID-CPA9>3.0.CO;2-Z Lieband, 1996 Myatt, 1997, Production of two overlapping Bose–Einstein condensates by sympathetic cooling, Phys. Rev. Lett., 78, 586, 10.1103/PhysRevLett.78.586 Ni, 1998, Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc., 45, 9 Ni, 1991, On the shape of least energy solution to a semilinear Neumann problem, Comm. Pure Appl. Math., 41, 819, 10.1002/cpa.3160440705 Ni, 1993, Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J., 70, 247, 10.1215/S0012-7094-93-07004-4 Ni, 1995, On the location and profile of spike-Layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math., 48, 731, 10.1002/cpa.3160480704 Timmermans, 1998, Phase separation of Bose–Einstein condensates, Phys. Rev. Lett., 81, 5718, 10.1103/PhysRevLett.81.5718 Troy, 1981, Symmetry properties in systems of semilinear elliptic equations, J. Differential Equations, 42, 400, 10.1016/0022-0396(81)90113-3 Wei, 1996, On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Differential Equations, 129, 315, 10.1006/jdeq.1996.0120 Wei, 1998, On the interior spike layer solutions to a singularly perturbed Neumann problem, Tohoku Math. J., 50, 159, 10.2748/tmj/1178224971 Wei, 2000, On the effect of the domain geometry in a singularly perturbed Dirichlet problem, Differential Integral Equations, 13, 15, 10.57262/die/1356124288 Wei, 1997, On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem, J. Differential Equations, 134, 104, 10.1006/jdeq.1996.3218 Wei, 1998, Stationary solutions for the Cahn–Hilliard equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 15, 459, 10.1016/S0294-1449(98)80031-0 Wei, 1999, Multiple boundary spike solutions for a wide class of singular perturbation problems, J. London Math. Soc., 59, 585, 10.1112/S002461079900719X